1. Field of the Invention
The present invention relates to a method for transporting alternate current in an armoured cable.
2. Description of the Related Art
An armoured cable is generally employed in application where mechanical stresses are envisaged. In an armoured cable, the cable core or cores (typically three stranded cores in the latter case) are surrounded by at least one metal layer in form of wires for strengthening the cable structure while maintaining a suitable flexibility.
When alternate current (AC) is transported into a cable, the temperature of electric conductors within, the cable rises due to resistive losses, a phenomenon referred to as Joule effect.
The transported current and the electric conductors are typically sized in order to guarantee that the maximum temperature in electric conductors is maintained below a prefixed threshold (e.g., below 90° C.) that guarantees the integrity of the cable.
The international standard IEC 60257-1-1 (second edition 200-12) provides methods for calculating permissible current rating of cables from details of permissible temperature rise, conductor resistance, losses and thermal resistivities. In particular, the calculation of the current rating in electric cables is applicable to the conditions of the steady-state operation at all alternating voltages. The term “steady state” is intended to mean a continuous constant current (100% load factor) just sufficient to produce asymptotically the maximum conductor temperature, the surrounding ambient conditions being assumed constant. Formulae for the calculation of losses are also given.
In IEC 60287-1-1, the permissible current rating of an AC cable is derived from the expression for the permissible conductor temperature rise Δθ above ambient temperature Ta, wherein Δθ=T−Ta, T being the conductor temperature when a current I is flowing into the conductor and Ta being the temperature of the surrounding medium under normal conditions, at a situation in which cables are installed, or are to be installed, including the effect of any local source of heat, but not the increase of temperature in the immediate neighbourhood of the cables to heat arising therefrom. For example, the conductor temperature T should be kept lower than about 90° C.
For example, according to IEC 60287-1-1, in case of buried AC cables where drying out of the soil does not occur or AC cables in air, the permissible current rating can be derived from the expression for the temperature rise above ambient temperature
                    I        =                              [                                                            Δ                  ⁢                                                                          ⁢                  θ                                -                                                      W                    d                                    ·                                      [                                                                  0.5                        ·                                                  T                          1                                                                    +                                              n                        ·                                                  (                                                                                    T                              2                                                        +                                                          T                              3                                                        +                                                          T                              4                                                                                )                                                                                      ]                                                                                                R                  ·                                      T                    1                                                  +                                  n                  ·                  R                  ·                                      (                                          1                      +                                              λ                        1                                                              )                                    ·                                      T                    2                                                  +                                  n                  ·                  R                  ·                                      (                                          1                      +                                              λ                        1                                            +                                              λ                        2                                                              )                                    ·                                      (                                                                  T                        3                                            +                                              T                        4                                                              )                                                                        ]                    0.5                                    (        1        )            whereI is the current flowing in one conductor (Ampere)Δθ is the conductor temperature rise above the ambient temperature (Kelvin)R is the alternating current resistance per unit length of the conductor at maximum operating temperature (Ω/m);Wd is the dielectric loss per unit length for the insulation surrounding the conductor (W/m);T1 is the thermal resistance per unit length between one conductor and the sheath (K·m/W);T2 is the thermal resistance per unit length of the bedding between sheath and armour (K·m/W);T3 is the thermal resistance per unit length of the external serving of the cable (K·m/W);T4 is the thermal resistance per unit length between the cable surface and the surrounding medium (K·m/W);n is the number of load-carrying conductors in the cable (conductors of equal size and carrying the same load);λ1 is the ratio of losses in the metal sheath to total losses in all conductors in that cable;λ2 is the ratio of losses in the armoring to total losses in all conductors in the cable.
In case of three-core cables and steel wire armour, the ratio λ2 is given, in IEC 60287-1-1, by the following formula:
                              λ          2                =                  1.23          ⁢                                    R              A                        R                    ⁢                                    (                                                2                  ⁢                                                                          ⁢                  c                                                  d                  A                                            )                        2                    ⁢                      1                                                            (                                                            2.77                      ⁢                                                                                          ⁢                                              R                        A                                            ⁢                                              10                        6                                                              ω                                    )                                2                            +              1                                                          (        2        )            where RA is the AC resistance of armour at maximum armour temperature (Ω/m);R is the alternating current resistance per unit length of conductor at maximum operating temperature (Ω/m);dA is the mean diameter of armour (mm);c is the distance between the axis of a conductor and the cable centre (mm);ω is the angular frequency of the current in the conductors.
The Applicant observes that, in general, the reduction of losses means reduction of the cross-section of the conductor/s and/or an increase of the permissible current rating.
In case of an armoured AC cable, the contribution of the armour losses to the overall cable losses has been investigated.
J. J. Bremnes et al (“Power loss and inductance of steel armoured multi-core cables: comparison of IEC values with “2.5D” FEA results and measurements”, Cigré, Paris, B1-116-2010) analyze armour loss in a three-core cable. They state that, for balanced three-phase currents, the collective armour will not allow any induced current flow in the armour wires due to cancellation by stranding/twisting. Any exception to this will require that the armour wires have exactly the same pitch as the cores, that the cable is very short, or that all armour wires are continuously touching both neighbouring wires. The authors state that this is in sharp contrast to the formulae for multi-core armour loss given in IEC 60287-1-1, in which the armour resistance RA is an important parameter. The authors state that, typically, for a three-core submarine cable, the IEC formula will assign 20-30% power loss to a collective steel armour, while their 2.5D finite element models and full scale measurements both predict insignificant power loss in the armour. G. Dell'Anna et al, (“HV submarine cables for renewable offshore energy”, Cigré, Bologna, 0241-2011) state that AC magnetic field induces losses in the armour and that hysteresis and eddy current are responsible for the losses generated into the armour. The authors show experimental results obtained by measuring the losses on a 12.3 m long cable, with a copper conductor of 800 mm2, and an outer diameter of 205 mm. The measurements were made for a current ranging from 20 A to 1600 A. FIG. 4 shows the measured values of the phase resistance, in two conditions with lead sheaths short circuited and armour present or completely removed. The phase resistance (that is the cable losses) is constant with the current in absence of armour, while it increases with current in presence of the armour. The authors state that the numerical value of the losses is important, especially for large conductor cables, but it is not as high as reported in IBC 60287-1-1 formulae.